N80-3344!TDA Progress Report 42-59 July and August 1980

Noise Adding Radiometer Performance AnalysisC. Stelzried

Radio Frequency and Microwave Subsystems Section

The DSN noise adding radiometer (NAR) measurement accuracy is analyzed. TheNAR capability is part of the Precision Power Monitor function recently introduced inthe DSN. The potential system noise temperature measurement accuracy is estimated tobe about 1.5% (la) with the 1 kelvin noise diode. Performance verification requires com-parison noise temperature measurements with the manual Y factor method and routinemonitoring of critical elements in the NAR system such as system linearity and noisediode calibration. A technique is presented to calibrate and reduce the effects of thereceiving system nonlinearity. Unsatisfactory performance or degradation of these criticalNAR elements would require appropriate system upgrading.

I. IntroductionA noise adding radiometer (NAR) is being implemented

(Fig. 1) in the DSN as an integral part of the Precision PowerMonitor (PPM). The NAR is required to convert signal-to-noiseratio (SNR) measurements to signal power. In addition theNAR is available with stand-alone capability.

II. TheoryThe fundamental equation for the NAR is (Refs. 1, 2):

'OP TJ(Y-1)N (1)

where

OP

T =N

system operating noise temperature, K (defined atsystem input reference plane)

noise diode injected noise temperature, K (definedat system input reference plane)

Y = (K2 ), ratio

V = detector output voltage, noise diode on, V

V = detector output voltage, noise diode off, V

a = detector nonlinearity constant, V"1 (=0 in an idealdetector)

The NAR noise temperature measurement resolution isgiven by Ref. 1.

where

T = measurement time, s

B = predetection bandwidth, Hz

For example,if TQp = 20 K,T = 10 s,.fi = 107 Hz, TN = 100 K,then

A70/>~0'005K

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TN can be calibrated by connecting the receiver input to theambient termination. With T p known, the NAR is used tosolve

T = T' OP AMB(r-i) (3)

using (assuming a perfectly matched system with transmission

(4)

line at temperature T )

'OP AMB + r

where

T = equivalent noise temperature of the receiver, K

= T + TJM IF

T = maser noise temperature, K

T = follow-up receiver noise temperature, K

T = physical temperature of ambient temperature, K

In the above, Tp is measured, TM* is assumed known fromlaboratory measurements and TF is determined from themaser on-off method.

T =* T IY1 F V oo (5)

where

Y = receiving system Y factor with maser turned offooand on, ratio

The calibration resolution of TN is given by (see Appendix A)

(6)

For example, if TQP = 300 K, T = 10 s, B = 107 Hz, TN =100 K, then

AT., = 0.08 K = 0.08%

However, if T'= 1 K in this example, then

0.06 K = 6%

which is unsuitable since a 6% error in TN results in a 6% errorin TOP, Eq. (1), (i.e., a "low" noise diode cannot be calibrateddirectly using the ambient termination technique with "short"integration time). If TN is small it is useful to use a larger TN

with a calibration transfer technique using both the ambienttermination and the antenna. This calibration technique con-sists of:

(1) Calibrating TNH using the ambient termination withEq. (4)

T - T* A

AMB( r - i ) (7)

(2) Calibrating the system operating noise temperature onthe antenna

OP ANT = T»J(Y- 1)'NH

(3) Calibrating T.. using the known T p from step 2

= TJ (r- i)

(8)

(9)

where

TNH = "high" noise diode, K

TNL = "low" noise diode, K

Using Eq. (6), the resolution of TNL (step 3 alone), assumingTOP = 20 K, r = 10 s, B = 107 Hz, TN = 1 K is 0.004 K.

Now, using TOP\AMB = 300 K, TOP\ANT = 20 K, TNH =100 K, TNL = 1 K, B = 107 Hz and going through the calibra-tion steps above, the calibration^resolution, using Eqs. (2) and(6), is

(1) = 0.025 K (r=100s)

(2) *TOPANT = 7(0.005)2* + (0.005)2** (T= 10s)

=* 0.007 Kand

(3) = >/(0.007)2 + (0.004)2 =« 0.01 K (T = 10 s)

This analysis neglects all bias errors and antenna/receiver sys-tem instabilities and interference. However, the analysis doesindicate the basic calibration resolution limit. A 1% resolution(0.01 K) can also be obtained with the low noise diode for thisexample by calibrating on the ambient termination directlyand integrating for approximately 6 minutes.

If TOP\ ~ 30° K and TM = 3 K., a 10% error in TM results inonly = 0.1%errorin7oJ (Refs. 3, 4).

•From Step 2, *Top\ = (&TNH)I(Y - 1) = 0.025/5 = 0.005 K.

**From Eq. (2).

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The primary "accuracy" concerns for the NAR are measure-ment resolution, repeatability as discussed above, bias errors,and "short" and "long" term measurement accuracy deteriora-tion. Measurement resolution is obtained by selecting the sys-tem operating parameters (primarily measurement time) tosatisfy Eq. (2). The primary concerns regarding bias errors andaccuracy deterioration are receiving system linearity and noisediode calibrations.

System non-linearity effects are analyzed in Appendix Band, for example (1), [TND(M)\AMB - TND(M^NT - 0.1

K], results in &TOP\ NT — 0.1. If the actual receiver non-linearity is unacceptable, lower the maser gain (results inhigher TE), upgrade the receiver, use algorithm equation B-3to reduce the effect or combine techniques to obtain accept-able performance.

III. NAR Performance

The expected noise temperature measurement accuracies(la) on the antenna for the NAR (assuming TOP\ =*20 K,

TOP\ MB - 300 K, B = 107 Hz and r = 10 s) are summarizedin Table 1 for 1 and 100 K noise diodes. It is assumed that thenoise diode waveguide coupler has satisfactory directivity. Thiscan be verified by TND(M)\AMB = TND(M)\ANT

maser gain.with reduced

The function of the NAR is to measure the receiving sys-tem operating noise temperature to a specified resolution andaccuracy at a prescribed data rate. A manual Y factor methodis available in the DSN for comparison noise temperaturemeasurements with the NAR. The manual method consists ofswitching the receiving input between the antenna and anambient termination and using a manually operated precision

IF waveguide beyond cutoff attenuator to measure the Yfactor. The la accuracy of the manual method is about 2 per-cent (Ref. 3).

Comparison of the NAR with the manual Y factor methodshould be performed on a routine basis to detect NAR degra-dation. In addition, the NAR performance is verified byroutine testing of the critical component elements of the NARsystem. These are:

(1) Measurement resolution (evaluate the noise tempera-ture measurement scatter).

(2) Linearity verification (using an auxiliary noise diodeon the antenna and ambient termination, Appendix B).

(3) Noise diode calibration (long-term noise temperaturecalibration monitoring).

The analysis summarized in Table 1 indicates that the NARhas about 1.5 percent (la) accuracy potential with the 1 Knoise diode (assuming no pathological problems such as RFinterference). This level of measurement accuracy requiresmonitoring of the critical measurement elements indicatedabove. This analysis assumes satisfactory performance of thesecritical NAR elements. Unsatisfactory performance (i.e.,unstable noise diode waveguide coupler or transmission lineconnectors, receiver nonlinearity, or RFI) would requireappropriate system upgrading.

Indication of unsatisfactory performance should be investi-gated by monitoring the noise diode calibration over a 24-hrperiod and correlating with ambient temperature. In addition,the system should be stressed by moving and braking theantenna, manual cable movement, etc.

Acknowledg ments

J. Hall suggested this study. B. Seidel, D. Bathker, L. Howard, and C. Foster made use-ful suggestions. J. Ohlson (Naval Postgraduate School, Monterey, Calif.) made suggestionsand verified concepts and analysis.

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Table 1. Summary of NAR measurement errors ofsystem noise temperature on the antenna

Case

Error source

Resolution, Eq. (2)

ATVCResolution,

1

0.08

0.20a

2

7jy=100K

0.005

0.016b

Eq. (6))

A Tobias error;assume 0.5%)

Receiver nonlinearity,Eq. (B-9) using 10 Kauxiliary noise diode

£ IerrorI

0.10

0.10

0.10

0.10

0.05(2.5%) 0.22(1.1%)

0.26(1.3%) 0.14(0.7%)

a Assumes A 7^ = 0.01 K.bAssumes &T - 0.08 K.

ANTENNA

WAVEGUIDESWITCH

AMBIENTTERMINATION

rDEFINEDREFERENCE PLANETOP' TN' TE

T0p (OUTPUT)

Fig. 1. Microwave receiving system showing NAR configuration

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Appendix A

Noise Diode Calibration Resolution

The NAR noise diode can be calibrated (assuming TOP isknown) using*

where

Vl = GTOP,V

G = system gain

¥ .Use

2T N =

= 7t|l + ^N

From total power radiometry theory,

V \2 1 aV " 2

(A-3)

where

B = bandwidth, Hz

^ r = total measurement time, s (measuring V. or F, only(A'2) 1/2 the time)

Then

*For calculation of resolution, a in Eq. (1) can be approximated as 0. N ~ N ' + OF N'' "*T

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Appendix B

Receiving System Linearity

Verification

The NAR system can be used with an auxiliary noise diodeto determine the receiving system nonlinearity. This is done byturning an auxiliary noise diode on and off with the receivingsystem connected alternately to the antenna and then to theambient termination. The degree of system nonlinearity isindicated by the difference between the increase in systemnoise temperature with the different input noise power levelsrepresented by the antenna and the ambient termination.

The auxiliary noise diode increases the system noise tem-perature by (receiving system input connected to the antennaor ambient termination, respectively)

ND -T.ANT ANT OPU

AMB- TV

AMB

ANT

AMB(B-2)

where

Tp = system operating noise temperature (auxiliary noiseQp

diode off), K

T = system operating noise temperature (auxiliary noiseQp

diode on), K

Assume that the corrected and measured system noise tem-peratures (Ref. 5) are related by (all measured temperaturesare identified by M)

-07*i00 (B-3)

Substituting Eq. (B-3) into (B-5) and solving using Eq. (B-7)

where

TOP(M) = measured system noise temperature, K

TOP = corrected system noise temperature, K

0 = system non-linearity factor, V"1 (= 0 in idealsystem)

y - system nonlinearity factor, ratio (= 1 in idealsystem)

Since

= 7\ANT AMB

we have

ANT- ANT~ T

AMB AMB(B-5)

From the NAR calibration technique, Eqs. (3) and (4),

= TVAMR AMB

. . , „ _ „and wrth Eq. B-3

7 = 1 + 0AMB

ft =.—AMB OP ND(M)\

(B-8)

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The error in TOP due to the system nonlinearity is (using&TOP = Tof - TOP(M), with Eqs. B-3 and B-7),

AMB- Tnp(M)} (B-9)

For example (1),

\ANT= 20K,r

OP AMB= 300 K,r (M)

ANT

= 10K,7\ = 10.1 K.AMB

This results in

0.10

(310.1) (10.1) + 300 (10) + (20)2 - (30)2

= 1.776X 10~s

7 = 1+(1.776 X 10~s) 300 =1.0053

A7OP I = 1.776 X 10"s (20) (300-20) = 0.1 K

This example is typical of a highly linear receiving system.

Equation (B-3) can be used as in the example for errorestimates or alternately as a method to reduce the effects ofthe receiving system nonlinearity. In the latter case, 0 and 7are determined from calibrations using the auxiliary noisediode and a corrected TOP is computed from Eq. (B-3). In this

case the linearity error is greatly reduced. This can be verifiedin practice with the same auxiliary noise diode.

For example (2)

ANT= 20 K, TOP\ AMB

= 300 K, TND(M)ANT

= 12 KAMB

This results in 0 ̂ 3.203 X 10"4,7 = 1.096 and A TOP\1.8 K. Equation (B-3) is shown plotted in Fig. B-l for thisexample, chosen to illustrate a highly nonlinear receivingsystem.

Poor directivity of the waveguide coupler used to inject thenoise diode, TN, could result in TND\ ANJ, * TND \ ̂ . Thisis due to the difference in coupling factor of the waveguidecoupler when connected to the antenna and ambient load,which in general will not have identical VSWRs. Therefore, ifTND ANT * TND(M}\ AMB

U wiU be necessary to distinguishbetween poor waveguide coupler directivity and receiver non-linearity. This can be done using an independent method fromthe above derivation for receiver linearity verification: (1) cali-brate system noise temperatures with normal system gain;(2) recalibrate system noise temperature, with reduced (ap-proximately 10 dB) maser gain accounting for increased maserfollowup noise temperature (Eq. 5). No change in the calibra-tions would indicate a linear system.

If low system noise temperature is not critical in a particu-lar application, then maser gain reduction could be a simpleoperational solution to receiver system nonlinearity.

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300

200

100

NONLINEAR RECEIVER.TOP = rlof(M) - ft Top

WM>|AMB= I2K

TND<M>|ANT. = IOK

0 = 3.203 x 10"4

T= 1.0V6

100 200

Top(M), K

300

Fig. B-1. Top vs 7^ (HI) for a highly nonlinear receiving system

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References

1. Batelaan P. D., Goldstein R. M.,and Stelzried, C. T., "A Noise Adding Radiometer forUse in the DSN," Space Programs Summary 37-65, Vol II, Jet Propulsion Laboratory,Pasadena, Calif.

2. Software Definition Document, DSS Receiver Subsystem Precision Power MonitorSDD-DOI-5132-OP Rev. A, Code ID No. 23835, Nov. 27, 1979.

3. Stelzried, C. T., "Operating Noise-Temperature Calibrations of Low-Noise ReceivingSystems," Microwave Journal, Vol. 14, No. 6, June 1971, p. 41.

4. Stelzried, C. T., "Post Amplifier Noise Temperature Contribution in a Low NoiseReceiving System," Proceedings of the IRE, Vol. 52, No. 1, Jan. 1964, p. 77.

5. Freiley, A. J., Ohlson, J. E., and Seidel, B. L., "Absolute Flux Density Calibrations:Receiver Saturation Effects," DSN Progress Report 42-46, May/June 1978, p. 123,Eq. (19), Jet Propulsion Laboratory, Pasadena, Calif.

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